Day 212 · Jul 30

The Law of Large Numbers

The Law of Large Numbers (first proved by Jacob Bernoulli) says that as the number of trials increases, the sample average converges to the expected value. Flip a fair coin 10 times: 70% heads? Possible. Flip 10,000 times: the proportion of heads will be very close to 50%. This justifies the frequency interpretation of probability. The law explains why casinos guarantee profits – the house edge becomes certain over millions of bets. It also justifies insurance premiums based on actuarial tables.

If you flip a coin 1,000 times, what is the approximate probability that the proportion of heads is between 0.48 and 0.52? (Hint: use normal approximation – standard deviation √(pq/n).)

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